Shrinkage strategies in some multiple multi-factor dynamical systems

Sévérien Nkurunziza
2012 E S A I M: Probability & Statistics  
In this paper, we are interested in estimation problem for the drift parameters matrices of m independent multivariate diffusion processes. More specifically, we consider the case where the mparameters matrices are supposed to satisfy some uncertain constraints. Given such an uncertainty, we develop shrinkage estimators which improve over the performance of the maximum likelihood estimator (MLE). Under an asymptotic distributional quadratic risk criterion, we study the relative dominance of the
more » ... ve dominance of the established estimators. Further, we carry out simulation studies for observation periods of small and moderate lengths of time that corroborate the theoretical finding for which shrinkage estimators outperform over the MLE. The proposed method is useful in model assessment and variable selection. Mathematics Subject Classification. 62M05, 58J65. X (i) (t) > 0, k = 1, 2, . . . , p and the real-valued functions V k X (i) (t) , k = 1, 2, . . . , p are such that the processes in (1.1) exist. Thereafter, we denote V X (i) (t) = V 1 X (i) (t) , V 2 X (i) (t) , . . . , V p X (i) (t) ,
doi:10.1051/ps/2010015 fatcat:b5hzwoyadfb4zmuzyy6lb2wsvy